Bicubic Filtering Implementation for Custom Data Types

Implementing bicubic sampling for your custom `Data` struct can be a bit challenging, but let’s break it down into manageable steps.

Understanding Bicubic Interpolation

Bicubic interpolation uses a weighted average of a 4×4 grid of pixels surrounding the target pixel. The weights are calculated based on the distances from the target pixel to each pixel in the grid. Here’s how you can start:

Step 1: Create a Weight Calculation Function

You need a function that computes the weights based on the relative distances. The general formula for bicubic weights is based on the cubic Hermite polynomials.

    float CubicWeight(float t) {
        if (t < 0) t = -t;
        if (t < 1) return (1.0f - 2.0f * t * t + t * t * t);
        if (t < 2) return (4.0f - 8.0f * t + 5.0f * t * t - t * t * t);
        return 0.0f;
    }
    

Step 2: Implement the Bicubic Sampling Function

Your function will take a texture coordinate and use it to find the relevant textures. You'll need to fetch 16 neighboring pixels (assuming you have some way to access them as `Data` types).

    template <typename T>
    T TImage<T>::BicubicSampling(const Math::Vec2& texCoord) const {
        // Get integer coordinates of the 4x4 grid
        int x = static_cast(texCoord.x);
        int y = static_cast(texCoord.y);
        
        // Calculate fractional offsets
        float xDiff = texCoord.x - x;
        float yDiff = texCoord.y - y;

        // Create an array for weights
        Data results[4][4];
        float weights[4][4];
        
        // Fetch the neighbors and calculate weights
        for (int i = -1; i <= 2; ++i) {
            for (int j = -1; j <= 2; ++j) {
                // Get neighbors here (be sure to handle texture edges)
                results[i + 1][j + 1] = GetTextureData(x + i, y + j); 
                weights[i + 1][j + 1] = CubicWeight(i - xDiff) * CubicWeight(j - yDiff);
            }
        }
        
        // Now perform the weighted average
        Data finalResult;
        float totalWeight = 0.0f;
        
        for (int i = 0; i < 4; ++i) {
            for (int j = 0; j < 4; ++j) {
                finalResult = finalResult + results[i][j] * weights[i][j];
                totalWeight += weights[i][j];
            }
        }
        
        // Normalize the result
        if (totalWeight > 0) {
            finalResult = finalResult * (1.0f / totalWeight);
        }
        
        return finalResult;
    }
    

Step 3: Edge Case Handling

Make sure your `GetTextureData` function properly handles edge cases, so you don't access out-of-bounds data in texture grids.

Conclusion

This is a basic outline of how to implement bicubic sampling for your `Data` struct. The key parts are calculating the weights and making sure to handle the additional complexity of arbitrary data types correctly. Test thoroughly and refine based on your needs!